⇄ — Inverse pair

Keys: Alt-4

f⇄g calls f. (f⇄g)⁻¹ is g⇄f.

f←{≥⍵}⇄{≤⍵} ⋄ f5            ⍝ 6
f←{≥⍵}⇄{≤⍵} ⋄ f⁻² 5        ⍝ 3

Dyadic inversion holds X fixed: X g (X f Y) must recover Y.

f←{⍺+⍵}⇄{⍵-⍺} ⋄ 3 f⁻¹ 8       ⍝ 5
f←{⍺+⍵}⇄{⍵-⍺} ⋄ (3↣f)⁻¹8      ⍝ 5

Left binding preserves the pair. For right binding, pair the bound monad: (f↢A)⇄undo.

See Power and Under.